Our maths education company (www.indexmatch.co.uk) is going from strength to strength, and we have more content coming soon, but I’ve been aware that our courses are for adults and not (currently) for children, and I’ve been wanting to find companies that have developed mathematical training for kids based on established scientific principles.
There are some great arithmetic products out there! Mostly, they focus on adaptive training and motivational factors, by which I mean they make the sums get harder in response to the ability of the child and create fun, playful environments. This is FANTASTIC, it has been reliably shown in numerous experiments that optimal learning happens when the task difficult is as hard as you can manage without failing. A useful analogy is to think about muscles, muscles get stronger fastest if you train at the limit of your ability!
One such company is www.mathsgarden.com, which, in collaboration with the University of Amsterdam, has created a online course for kids based on exactly this kind of adaptive training. A great benefit of this approach when used within schools is that the teacher has excellent data on the performance of each child, without having to do the marking and so has more time to engage one-on-one with children that need help.
IndexMatch seems to be one of very few companies that provide training in mathematics rather than arithmetic. Another notable company is Wolfram (http://www.wolfram.com/training/courses/education/) who have created Wolfram Alpha and Mathematica in order that people can engage in mathematics and not arithmetic.
More on them next time, but for a quick experiment try typing “Am I drunk?” into Wolfram Alpha (http://www.wolframalpha.com)!